To find the solution to the equation [tex]\( \frac{24 - 3}{3x - 5} = 23 \)[/tex]:
### Step-by-Step Solution:
1. Simplify the given equation:
[tex]\[\frac{24 - 3}{3x - 5} = 23\][/tex]
First, simplify the numerator: [tex]\(24 - 3 = 21\)[/tex]. Thus, the equation becomes:
[tex]\[\frac{21}{3x - 5} = 23\][/tex]
2. Isolate the fraction:
To isolate [tex]\(3x - 5\)[/tex] in the denominator, multiply both sides of the equation by [tex]\(3x - 5\)[/tex]:
[tex]\[21 = 23(3x - 5)\][/tex]
3. Distribute the 23 on the right-hand side:
[tex]\[21 = 69x - 115\][/tex]
4. Isolate the variable term [tex]\(69x\)[/tex]:
Add 115 to both sides to move the constant term to the left:
[tex]\[21 + 115 = 69x\][/tex]
[tex]\[136 = 69x\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Divide both sides by 69 to isolate [tex]\(x\)[/tex]:
[tex]\[x = \frac{136}{69}\][/tex]
Thus, the solution to the equation [tex]\(\frac{24 - 3}{3x - 5} = 23\)[/tex] is:
[tex]\[\boxed{\frac{136}{69}}\][/tex]
